OPTIMAL TAX POLICY FOR A SINGLE HOMOGENEOUS COMMODITY ON TWO MARKETS WITH EXPORT COSTS AS A BILEVEL PROGRAMMING PROBLEM

Taxation is one of the most powerful instruments of fiscal policy, having important implications on supply and demand, affecting economic growth and investments as well as the competitiveness of companies operating under a given tax policy. It also affects a company’s incentive to stay or to move its operations elsewhere. Therefore, designing the optimal tax policy is of crucial importance for any government. This study considers the problem of determining optimal tax policy for a single homogeneous commodity produced by two competing companies located in two different countries. Each company has one manufacturing facility located in its country of origin, while the product is sold in both countries. Countries have different tax systems. If a company sells the product on a foreign market, in addition to the cost of production there is also an export cost, which consists of transportation cost and duty cost. The problem is modelled as a bilevel programming problem with two followers, where the leader (the government) maximizes the tax revenue, whereas followers (companies) maximize their profit functions. In addition to formulating a new model that is not known in the existing literature so far, the paper derives the optimal tax level and the corresponding maximum amount of tax revenue, as well as the optimal production and export levels for the companies. It discusses the properties of the profit function and the impact of increasing taxes on optimal quantities and revenue and profit functions of the companies. Finally, it shows how the burden of tax is divided between producers and consumers. The model is illustrated by numerical example.